Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
598 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22599458 | C2 | semidirect |
| 3. #22598799 | C2 | semidirect |
| 4. #22589292 | C2 | semidirect |
| 5. #22586834 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1980 | C2 | semidirect |
| 118. M16×C71 | D8 | semidirect |
| 208. #1980 | D71 | semidirect |
| 211. C71 | #10204 | semidirect |
| 311. M16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599647 | 2 |
| #22599458 | 2 |
| #22598799 | 2 |
| #22589292 | 2 |
| #22586834 | 2 |
| #22586191 | 2 |
| C71×#1980 | 2 |
| #10204 | 71 |